The concentration of paramagnetic trace impurities in glasses can be determined via precise SQUID measurements of the samples magnetization in a magnetic field. However the existence of quasi-ordered structural inhomogeneities in the disordered solid
causes correlated tunneling currents that can contribute to the magnetization, surprisingly, also at the higher temperatures. We show that taking into account such tunneling systems gives rise to a good agreement between the concentrations extracted from SQUID magnetization and those extracted from low-temperature heat capacity measurements. Without suitable inclusion of such magnetization contribution from the tunneling currents we find that the concentration of paramagnetic impurities gets considerably over-estimated. This analysis represents a further positive test for the structural inhomogeneity theory of the magnetic effects in the cold glasses.
The thermal and dielectric anomalies of window-type glasses at low temperatures ($T<$ 1 K) are rather successfully explained by the two-level systems (2LS) standard tunneling model (STM). However, the magnetic effects discovered in the multisilicate
glasses in recent times, magnetic effects in the organic glasses and also some older data from mixed (SiO$_2$)$_{1-x}$(K$_2$O)$_x$ and (SiO$_2$)$_{1-x}$(Na$_2$O)$_x$ glasses indicate the need for a suitable extension of the 2LS-STM. We show that -- not only for the magnetic effects, but already for the mixed glasses in the absence of a field -- the right extension of the 2LS STM is provided by the (anomalous) multilevel tunnelling systems (A-TS) proposed by one of us for multicomponent amorphous solids. Though a secondary type of TS, different from the standard 2LS, was invoked long ago already, we clarify their physical origin and mathematical description and show that their contribution considerably improves the agreement with the experimental data.
The dielectric anomalies of window-type glasses at low temperatures ($T<$ 1 K) are rather successfully explained by the two-level systems (2LS) tunneling model (TM). However, the magnetic effects discovered in the multisilicate glasses in recent time
s cite{ref1}-cite{ref3}, and also some older data from mixed (SiO$_2$)$_{1-x}$(K$_2$O)$_x$ and (SiO$_2$)$_{1-x}$(Na$_2$O)$_x$ glasses cite{ref4}, indicate the need for a suitable generalization of the 2LS TM. We show that, not only for the magnetic effects cite{ref3,ref5} but also for the mixed glasses in the absence of a field, the right extension of the 2LS TM is provided by the (anomalous) multilevel tunneling systems approach proposed by one of us. It appears that new 2LS develop via dilution near the hull of the SiO$_4$-percolating clusters in the mixed glasses.
A quantum pseudo-spin model with random spin sizes is introduced to study the effects of charging-energy disorder on the superconducting transition in granular superconducting materials. Charging-energy effects result from the small electrical capaci
tance of the grains when the Coulomb charging energy is comparable to the Josephson coupling energy. In the pseudo-spin model, randomness in the spin size is argued to arise from the inhomogeneous grain-size distribution. For a particular bimodal spin-size distribution, the model describes percolating granular superconductors. A mean-field theory is developed to obtain the phase diagram as a function of temperature, average charging energy and disorder.
Puzzling observations of both thermal and dielectric responses in multi-silicate glasses at low temperatures $T$ to static magnetic fields $B$ have been reported in the last decade and call for an extension of the standard two-level systems tunneling
model. An explanation is proposed, capable of capturing at the same time the $T$- and $B$-dependence of the specific heat $C_p$ and of the dielectric constant $epsilon$ in these glasses. This theory points to the existence of anomalous multi-welled tunneling systems in the glasses -- alongside the standard two-level systems -- and indications are given for glasses which should achieve larger electric magnetocapacitive enhancements.
